Maximization of capacity and l(p) norms for some product channels

It is conjectured that the Holevo capacity of a product channel Omegacircle timesPhi is achieved when product states are used as input. Amosov, Holevo, and Werner have also conjectured that the maximal l(p) norm of a product channel is achieved with product input states. In this article we establish both of these conjectures in the case that Omega is arbitrary and Phi is a CQ or QC channel (as defined by Holevo). We also establish the Amosov, Holevo and Werner conjecture when Omega is arbitrary and either Phi is a qubit channel and p=2, or Phi is a unital qubit channel and p is integer. Our proofs involve a new conjecture for the norm of an output state of the half-noisy channel Icircle timesPhi, when Phi is a qubit channel. We show that this conjecture in some cases also implies additivity of the Holevo capacity. (C) 2002 American Institute of Physics.